Question

The roots of the following quadratic equation are not real

$\frac{3}{5}{x}^2-\frac{3}{5}x+1$

• A. True
• B. False

Answer 1

The correct option is A True

$\frac{3}{5}{x}^2-\frac{3}{5}x+1=0$

$\Rightarrow$ $3x^2-3x+5=0$

$\Rightarrow$ $a=3,b=-3,c=5$

$\Rightarrow$ $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$=\frac{-(-3)\pm \sqrt{(-3{)}^2-4(3\left)\right(5)}}{2\left(3\right)}$

$=\frac{3\pm \sqrt{9-60}}{6}$

$=\frac{3\pm \sqrt{-51}}{6}$

$=\frac{3\pm \sqrt{51}i}{6}$

$\therefore$ $x=\frac{3+\sqrt{51}i}{6}$ and $x=\frac{3-\sqrt{51}i}{6}$

$\therefore$ We can see roots are not real.